The present invention is directed to magnetic resonance imaging (MRI) apparatus and methods, and particularly to apparatus and methods which increase the accuracy and/or resolution of MRI images, and/or decrease the time required to obtain an MRI image.
MRI is based on solving the Bloch Equations
dMx/dt=xe2x88x92xcex3HzMyxe2x88x92Mx/T2,xe2x80x83xe2x80x83(1.1)
dMy/dt=xe2x88x92xcex3HzMxxe2x88x92My/T2,xe2x80x83xe2x80x83(1.2)
and
dMz/dt=xe2x88x92(M0xe2x88x92Mz)/T1,xe2x80x83xe2x80x83(1.3)
which gives the magnetization M=Mxx+Myy+Mzz of magnetic nuclei (typically protons) in the presence of a magnetic field H=Hzz. Standard nuclear magnetic resonance (NMR) uses a homogeneous magnetic field, but to obtain the spatial resolution required for image mapping, gradient magnetic fields must be added. The interaction of the magnetic spins with the environment is given in terms of the transverse relaxation time T2 which determines the rate of decay of the Mx and My components of the magnetization M to zero, and the longitudinal relaxation time T1 which determines the rate of decay of the Mz component of the magnetization M to the value M0. It has been previously shown (Prolongation of Proton Spin Lattice Relaxation Times in Regionally Ischemic Tissue from Dog Hearts, E. S. Williams, J. I. Kaplan, F. Thatcher, G. Zimmerman and S. B. Knoebel, Journal of Nuclear Medicine, May 1980, Vol. 21, No. 5) that T1 is different in normal and ischemic heart muscle by about 10%. Using the inversion recovery technique (which is described in detail in U.S. Pat. No. 4,383,219, entitled Nuclear Magnetic Resonance Spatial Mapping, issued May 10, 1983 to Jerome I. Kaplan, and is incorporated herein by reference) the 10% difference in the relaxation times can be amplified into a 25% differentiation in the magnetization in the normal and ischemic regions of the heart. Thus mapping this difference in magnetization allows for a mapping of the normal and ischemic regions of the heart.
High-resolution MRI images of non-moving body parts are routinely obtained. However, an added difficulty with the heart arises from its large scale rapid motion at about one beat per second. To avoid blurring, the MRI image must therefore be obtained in less than {fraction (1/20)}th of a second.
As is shown in the present specification, standard mapping procedures do not permit a high-resolution mapping for times of less than {fraction (1/20)}th of a second. An advantage of the present invention is that high-resolution images may be obtained for mappings where the data is acquired in a short period of time.
The mapping procedure of the present invention is as follows:
1) A radio frequency pulse or pulse sequence rotates the magnetization M(x,y) of the actual object density xcfx81(x,y) from its equilibrium direction along the z-axis (i.e., the direction of the large applied static magnetic field) to the x-y plane. The magnetization M(x,y) precesses at a frequency xcfx89(x,y) about the local gradient fields at position (x,y).
2) The total magnetization is recorded by monitoring the induced voltage in the receiver coils. The relation between the total magnetization M and the actual object density xcfx81(x,y) is described by the transform F(t,x,y) according to
M(t)=∫F(t,x,y)xcfx81(x,y)dxdy,xe2x80x83xe2x80x83(1.4)
3) An estimated mapping object density xcfx81*(x,y) is obtained from the magnetization M(t) by application of a transform E according to
xcfx81*(x,y)=xcexa3tE(t,x,y)M(t).xe2x80x83xe2x80x83(1.5)
For long mapping times, the estimated object density xcfx81*(x,y) is a relatively accurate map of the actual object density xcfx81(x,y) using this standard procedure. However, for shorter mapping times, the estimated object density xcfx81*(x,y) becomes a less accurate mapping of the actual object density xcfx81(x,y).
In a first preferred embodiment, the present invention therefore includes the following additional steps:
4A) A kernel function A which describes the relationship between the estimated object density xcfx81*(x,y) and the actual object density xcfx81(x,y) is estimated, i.e.,
xcfx81*(x,y)=∫A(x,y,xxe2x80x2yxe2x80x2)xcfx81(xxe2x80x2,yxe2x80x2)dxxe2x80x2dyxe2x80x2,xe2x80x83xe2x80x83(1.6)
xe2x80x83where the kernel function is given by
A(x,y,xxe2x80x2yxe2x80x2)=xcexa3tE(t,x,y)F(t,xxe2x80x2,yxe2x80x2).xe2x80x83xe2x80x83(1.7)
5A) The kernel function A is discretized to form a kernel matrix B describing the relationship between the estimated object density pixel values xcfx81*(x,y) and the actual object density pixel values xcfx81(x,y), i.e.,                                           ρ            *                    ⁡                      (                          x              ,              y                        )                          =                              ∑                                          x                xe2x80x2                            ,                              y                xe2x80x2                                              ⁢                                    B              ⁡                              (                                  x                  ,                  y                  ,                                      x                    xe2x80x2                                    ,                                      y                    xe2x80x2                                                  )                                      ⁢                                          ρ                ⁡                                  (                                                            x                      xe2x80x2                                        ,                                          y                      xe2x80x2                                                        )                                            .                                                          (        1.8        )            
6A) The inverse of the kernel matrix B is applied to the estimated object density xcfx81*(x,y) to produce an increased-accuracy object density xcfx81**(x,y) which more accurately represents the actual object density xcfx81(x,y), i.e.,                                           ρ            **                    ⁡                      (                          x              ,              y                        )                          =                              ∑                                          x                xe2x80x2                            ,                              y                xe2x80x2                                              ⁢                                                    B                                  -                  1                                            ⁡                              (                                                      x                    xe2x80x2                                    ,                                      y                    xe2x80x2                                                  )                                      ⁢                                                            ρ                  *                                ⁡                                  (                                                            x                      xe2x80x2                                        ,                                          y                      xe2x80x2                                                        )                                            .                                                          (        1.9        )            
This procedure allows for high-resolution mapping of a moving subject, such as an organ like the heart. It should also be noted that the application of the inverse of the kernel matrix B to the estimated object density xcfx81*(x,y) to provide the increased-accuracy object density xcfx81**(x,y) is also useful in producing increased accuracy images in situations where there are no time constraints.
In a second preferred embodiment of the present invention, information regarding the object density is utilized to increase the accuracy of the estimate of the transform E(t,x,y). The second preferred embodiment of the present invention therefore includes the following additional steps:
4B) Ischemic and normal regions of the myocardium are mapped according to the estimated object density xcfx81*(x,y).
5B) The transform E(t,x,y) is corrected to form corrected transform Ec(t,x,y) based on the locations of the ischemic and normal regions of the myocardium obtained from the estimated object density xcfx81*(x,y).
6B) The corrected transform Ec(t,x,y) is used to calculate a corrected estimated object density xcfx81c*(x,y) according to
xcfx81c*(x,y)=xcexa3tEc(t,x,y)M(t).xe2x80x83xe2x80x83(1.10)
According to a third preferred embodiment of the present invention a combination of the techniques of the first two preferred embodiments is used. The process of the third preferred embodiment of the present invention includes a modification of step 3, described above, as follows:
3C) A current-best estimated object density xcfx81b*(x,y) is obtained from the magnetization M(t) by application of a current-best transform Eb according to
xcfx81b*(x,y)=xcexa3tEb(t,x,y)M(t).xe2x80x83xe2x80x83(1.11)
The currently-best transform Eb is based on an average value of the actual object density xcfx81, unless a corrected transform Ec based on an estimation of the normal and ischemic regions has been calculated. Furthermore, the process of the third preferred embodiment of the present invention includes the following steps:
4C) When an estimated object density xcfx81*(x,y) is calculated or updated to provide a current-best estimated object density xcfx81b*(x,y), then a choice is made to either (i) use the current-best estimated object density xcfx81b*(x,y) to produce an estimate of the ischemic and normal regions, as described in step 6C below, or (ii) use the current-best estimated object density xcfx81b*(x,y) to produce a current-best corrected object density xcfx81b**(x,y), as described in step 5C below.
5C) The inverse of a best kernel matrix Bb is applied to the current-best estimated object density xcfx81b*(x,y) to produce a current-best increased-accuracy object density xcfx81b**(x,y), which more accurately represents the actual object density xcfx81(x,y), according to                                                         ρ              b              **                        ⁡                          (                              x                ,                y                            )                                =                                    ∑                              k                ,                l                                      ⁢                                                            [                                                            B                      b                                        ⁡                                          (                                              x                        ,                        y                        ,                                                  x                          xe2x80x2                                                ,                                                  y                          xe2x80x2                                                                    )                                                        ]                                                  -                  1                                            ⁢                                                ρ                  b                  *                                ⁡                                  (                                      x                    ,                    y                                    )                                                                    ,                            (        1.12        )            
where the current-best kernel matrix Bb uses the inital estimate of the transform E based on an average value of the actual object density xcfx81, unless a corrected transform Ec based on estimated normal and ischemic regions has been calculated.
OR
6C) Ischemic and normal regions of the myocardium are mapped based on the current-best estimated object density xcfx81b*(x,y) or the current-best improved-accuracy object density xcfx81b**(x,y)
7C) A corrected transform Ec(t,x,y) is calculated based on current-best estimation of the ischemic and normal regions of the myocardium.
Therefore, it is an object of the present invention to provide apparatus and method for magnetic resonance imaging which increases the accuracy of magnetic resonance images.
It is another object of the present invention to provide apparatus and method for magnetic resonance imaging which improves the spatial resolution of magnetic resonance images.
It is another object of the present invention to provide apparatus and method for magnetic resonance imaging which decreases the time required to obtain magnetic resonance images.
It is another object of the present invention to provide apparatus and method for utilizing information regarding ischemic and normal regions of the myocardium in the improvement of the spatial resolution of magnetic resonance images and/or the reduction in time required to obtain magnetic resonance images.
It is another object of the present invention to provide method and apparatus of efficient solution of an increased-accuracy object density.
It is another object of the present invention to provide method and apparatus of solution of an increased-accuracy object density for regions where relationships between actual object density and estimated object density are roughly translationally invariant.
Further objects and advantages of the present invention will become apparent from a consideration of the drawings and the ensuing detailed description.
The present invention is directed to a method for producing increased-accuracy object density ** of an object from estimated object density * by compensating for a spatial mixing of object density data involved in an initial estimation of the object density from the magnetization data. Data values M extracted from the object are related to the integration of the actual object density  over one-, two-, or three-dimensional space with a weighting by a transform function F, i.e.,
M(t)=∫F(q,t)(q)dq,xe2x80x83xe2x80x83(2.1.1)
where q is a coordinate vector in the space. The estimated object density * is related to the data values M(t) by the transform,
*(q)=xcexa3tE(q,t)M(t),xe2x80x83xe2x80x83(2.1.2)
where transform E(q,t). Therefore, the actual object density is related to the estimated object density by the relationship
*(q)=∫A(q,qxe2x80x2)(qxe2x80x2)dqxe2x80x2,xe2x80x83xe2x80x83(2.1.3)
where A(q,qxe2x80x2) is a kernel function given by
A(q,qxe2x80x2)=xcexa3tF(qxe2x80x2,t)E(q,t),xe2x80x83xe2x80x83(2.1.4)
which approximates, but is not equal to, a delta function xcex4(qxe2x88x92qxe2x80x2), and therefore values of the actual object density (qxe2x80x2) away from qxe2x80x2=q contribute to *(q). The increased-accuracy object density ** is obtained by the relationship
**(q)=xcexa3qxe2x80x2Bxe2x88x921(q,qxe2x80x2)(qxe2x80x2),xe2x80x83xe2x80x83(2.1.5)
where B(q,qxe2x80x2) is a discretized version of A(q,qxe2x80x2).
The present invention is also directed to a method for producing a correction in the calculation of an approximation of the actual object density  based on magnetization data M using object density approximations to estimate the normal and ischemic regions. Magnetization data values M extracted from the object are related to the integration of the actual object density  over one-, two-, or three-dimensional space via transform function F according to
M(t)=∫F((q),q,t)(q)dq,xe2x80x83xe2x80x83(2.2.1)
where q is a coordinate vector in the space. The estimated object density * is related to the data values M(t) by the transform,
*(q)=xcexa3tE([],q,t)M(t),xe2x80x83xe2x80x83(2.2.2)
where the square brackets indicate that a characteristic value of the variable within is used. Using the estimated object density *(q), a corrected transform Ec is generated, i.e.,
Ec=E(*(q),q,t).xe2x80x83xe2x80x83(2.2.3)
Corrected estimated object density pixel values c* are then calculated according to
c*(q)=xcexa3tEc(t)M(t).xe2x80x83xe2x80x83(2.2.4)
Furthermore, the present invention is directed to a method for producing second (or even higher) order corrections in the calculation of an approximation of the actual object density  based on magnetization data M using object density approximations to estimate the normal and ischemic regions and, optionally, compensating for a spatial mixing of object density data involved in an initial estimation of the object density from the magnetization data. Data values M extracted from the object are related to the integration of the actual object density  over one-, two-, or three-dimensional space q with a weighting by a transform function F, i.e.,
M(t)=∫F(,q,t)(q)dq.xe2x80x83xe2x80x83(2.3.1)
An estimated object density * is related to the data values M by the transform,
*(q)=xcexa3tE([],q,t)M(t),xe2x80x83xe2x80x83(2.3.2)
where the square brackets indicate that a characteristic value of the variable within is used. Therefore, the estimated object density * is related to the actual object density  by
*(q)=∫A(q,qxe2x80x2)(qxe2x80x2)dqxe2x80x2,xe2x80x83xe2x80x83(2.3.3)
where A(q,qxe2x80x2) is a kernel function given by
A(q,qxe2x80x2)xe2x89xa1xcexa3tE([],q,t)F((qxe2x80x2),qxe2x80x2,t),xe2x80x83xe2x80x83(2.3.4)
which approximates, but is not equal to, a delta function xcex4(qxe2x88x92qxe2x80x2), and therefore values of the actual object density (qxe2x80x2) away from qxe2x80x2=q contribute to *(q). An increased-accuracy object density ** is obtained by the relationship
**(q)=xcexa3qxe2x80x2Bxe2x88x921(q,qxe2x80x2)(qxe2x80x2),xe2x80x83xe2x80x83(2.3.5)
where B(q,qxe2x80x2) is a discretized version of A(q,qxe2x80x2). Using the increased-accuracy object density **(q), a corrected transform Ec is generated, i.e.,
Ec=E(**(q),q,t).xe2x80x83xe2x80x83(2.3.6)
A corrected increased-accuracy object density c** is then calculated according to
c*(q)=xcexa3tEcM(t).xe2x80x83xe2x80x83(2.3.7)
The present invention is also directed to a method for producing a correction in the calculation of an approximation of the actual object density  based on magnetization data M using object density approximations to estimate the normal and ischemic regions. Magnetization data values M extracted from the object are related to the integration of the actual object density  over one-, two-, or three-dimensional space via transform function F according to
M(t)=∫F((q),q,t)(q)dq,xe2x80x83xe2x80x83(2.4.1)
where q is a coordinate vector in the space. The estimated object density * is related to the data values M(t) by the transform,
*(q)=xcexa3tE([],q,t)M(t),xe2x80x83xe2x80x83(2.4.2)
where the square brackets indicate that a characteristic value of the variable within is used. Using the estimated object density *(q), a corrected transform Ec is generated, i.e.,
Ec=E(*(q),q,t).xe2x80x83xe2x80x83(2.4.3)
Corrected estimated object density pixel values c* are then calculated according to
c*(q)=xcexa3tEcM(t).xe2x80x83xe2x80x83(2.4.4)
Using the corrected estimated object density c*(q), a second-order corrected transform Ecc is generated, i.e.,
Ecc=E(c*(q),q,t),xe2x80x83xe2x80x83(2.4.5)
and a second-order corrected estimated object density cc* is then calculated according to
cc*(q)=xcexa3tEccM(t).xe2x80x83xe2x80x83(2.4.6)
The present invention is also directed to a method for producing a correction in the calculation of an approximation of the actual object density  based on magnetization data M using object density approximations to estimate the normal and ischemic regions. Magnetization data values M extracted from the object are related to the integration of the actual object density  over one-, two-, or three-dimensional space via transform function F according to
M(t)=∫F((q),q,t)(q)dq,xe2x80x83xe2x80x83(2.5.1)
where q is a coordinate vector in the space. The estimated object density * is related to the data values M(t) by the transform,
*(q)=xcexa3tE([],q,t)M(t),xe2x80x83xe2x80x83(2.5.2)
where the square brackets indicate that a characteristic value of the variable within is used. Using the estimated object density *(q), a corrected transform Ec is generated, i.e.,
xe2x80x83Ec(q,t)=E(*(q),q,t).xe2x80x83xe2x80x83(2.5.3)
Corrected estimated object density pixel values c* are then calculated according to
c*(q)=xcexa3tEc(q,t)M(t).xe2x80x83xe2x80x83(2.5.4)
A corrected kernel function Ac(q,qxe2x80x2) is given by
Ac(q,qxe2x80x2)=xcexa3tF(qxe2x80x2,t)Ec(q,t),xe2x80x83xe2x80x83(2.5.5)
and an increased-accuracy corrected object density c** is obtained by the relationship
c**(q)=xcexa3qxe2x80x2[Bc(q,qxe2x80x2)]xe2x88x921c*(qxe2x80x2),xe2x80x83xe2x80x83(2.5.6)
where Bc(q,qxe2x80x2) is a discretized version of Ac(q,qxe2x80x2).